Abstract
Let G be a finite non-abelian group and Z(G) be its center. We associate a commuting graph \(\Gamma (G)\) to G, whose vertex set is \(G\setminus Z(G)\) and two distinct vertices are adjacent if they commute. In this paper we prove that the set of all non-abelian groups whose commuting graph has maximum vertex degree bounded above by a fixed \(k \in {\mathbb {N}}\) is finite. Also, we characterize all groups for which the associated commuting graphs have maximum vertex degree at most 4.
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The authors would like to thank the anonymous referee for carefully reading this paper.
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Bhunia, S., Arunkumar, G. Groups with maximum vertex degree commuting graphs. Indian J Pure Appl Math 55, 234–241 (2024). https://doi.org/10.1007/s13226-022-00359-x
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DOI: https://doi.org/10.1007/s13226-022-00359-x